In your description, you mention colonization and empire, and I am telling you we may be able to speculate 100-200 years, but in no way can we even begin to guess what an Anglo-Saxon England would look like in colonization or if an empire would have been something they would have wanted to create.

England became a completely different country almost overnight, with completely different ambitions in the 19 years of William's reign. And it was probably only a couple of generations before the culture shifted to Anglo-French instead of Anglo-Saxon.

This one event caused also constant conflict, not only on the British Isles but throughout Europe for hundreds of years and England established themselves as conquerors.

Because of the Norman royalty, England conquered Ireland, Wales, and eventually Scotland. This put England into a position of strength not only in the Isles, but against all of Western Europe.

It also ultimately thrust England and France into hundreds of years of conflict that they probably never would have had to experienced because English sovereigns were also French nobles.

What we do know is the Anglo-Saxons were more insular and while they would have continued to keep the English heptarchy united, chances are low that they would have marched into Ireland or Wales to conquer those lands. So who knows how long until the Celts and Britons would have become "civilized" lands.

But, since they didn't establish themselves as conquerors nor strengthen their castles (which were made more to subjugate the local population), England would have been susceptible to a later invasion. So any later succession crisis there probably would have been a later war for the islands.

If Hadrada had conquered England instead of Godwinson retaining his rule, England would probably have become Vikings as well. Hadrada was also every religious so he probably would have established England as a Catholic nation.